Works and Documented

src/LFO/lfo_freq_square.m

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+function output = lfo_freq_square(amplitude, frequency, phase, fs, duration, input)
+%LFO_FREQ_SQUARE Modulates the frequency of an input with a square LFO
+
+% CONTRIBUTORS:
+% Neelay Joglekar: Original author
+
+% SOURCES:
+% Code inspired by Benjamin Liou's lfo functions
+% Code also inspired by Darren and Anne's pitch envelopes
+% Source for frequency modulation equation:
+%   https://dsp.stackexchange.com/questions/2349/help-with-algorithm-for-modulating-oscillator-pitch-using-lfo
+
+% DOCUMENTATION:
+% Frequency is modulated by square wave with given amplitude (in octaves, not Hz)
+
+    % initialize local variables from input arguments
+    n = fs * duration; % number of samples (length of matrix)
+    dt = 1 / fs; % sampling period: time between two sample points
+
+    % create output array
+    output = zeros([1, n]);
+    
+    x = 0.0; % the theoretical input index if the input were not discrete
+    % populate output
+    for i = 1:n
+        t = i * dt; % time at the i'th sample
+
+        % Increment x based off of square wave output
+        omega_ratio = 2 ^ (amplitude * (2 * round(mod((t - phase / (2*pi)) * frequency, 1)) - 1));
+        x = mod(x + omega_ratio, n);
+
+        % Linearly interpolate the actual indicies adjacent to x
+        % to get an output value
+        x_0 = floor(x) + 1;
+        x_1 = mod(x_0 + 1, n) + 1;
+        output(i) = (input(x_1) - input(x_0)) * (x - x_0) + input(x_0);
+    end
+end